Pole assignment in a specified disk.

*(English)*Zbl 0627.93029An algorithm to assign all poles of the closed-loop system in the disk D with the center on the real axis of the complex plane and arbitrary radius for both continuous and discrete systems is studied. A state feedback control law is also determined using a discrete Riccati equation. This kind of pole assignment problem is named D-pole assignment. The advantages of the D-pole assignment are presented using some simple proofs of theorems and lemmas. The gain margin of the discrete optimal control is given by a proof different from that already given by M. G. Safonov [Stability and robustness of multivariable feedback systems, The MIT Press, XI (1980; Zbl 0552.93002)]. To illustrate D-pole assignment an example is given. In this example the proposed algorithm gives D-pole assignment and the pole locations within the specified disk D, depending on the matrices Q, R of the Riccati equation.

The paper is well organized and written and can be considered to be of very good quality in its topic area.

The paper is well organized and written and can be considered to be of very good quality in its topic area.

Reviewer: A.Machias

##### MSC:

93B55 | Pole and zero placement problems |

15A24 | Matrix equations and identities |

93C05 | Linear systems in control theory |

93C55 | Discrete-time control/observation systems |